The peer's combination of strong Tory credentials and a reputation burnished by the success of the Games have made him frontrunner to succeed Lord Patten. Coe is said to have the firm support of David Cameron, according to ITV News political editor Tom Bradby. The prime minister is ultimately responsible for ratifying the appointment.

Coe's spokeswoman did not explicitly rule out his potential interest in the role, but did say he is frequently raised as a prospect for high-profile jobs.

"Seb is linked to every job in London and this is another one," said Susie Black, personal assistant to Coe. "This is speculation at the moment."

Boris Johnson immediately lent his support to Coe. The London mayor called him a "first rate choice" for the role.

"I think it's fantastic news for the BBC and British broadcasting," he said, speaking to ITV News. "Seb Coe is a great leader. I've worked with him a lot over the last few years and I think he'll demand very high standards of the BBC but I think he'll be in exactly the right tradition of British broadcasting. It's a first rate choice."

The £110,000-a-year, four days a week job has not yet been advertised, but the Department for Culture, Media and Sport is understood to have appointed headhunters to help define the scope of the role and identify the best candidates.

While the official process is yet to start, candidates on a list being compiled by senior officials include Dame Marjorie Scardino, the former chief executive of the company behind the Financial Times, and Colette Bowe, the former chair of the broadcasting regulator Ofcom.

Coe is not thought to have held a serious meeting about his candidacy. However he already has a previous working relationship with BBC director general Tony Hall.

In 2009, Hall, then chief executive of the Royal Opera House, was asked to chair a board to direct the Cultural Olympiad.

This gave Hall a seat on the board of the London Organising Committee for the Olympic Games, which Coe chaired.

One source said Coe's "knitting together" of cross-party political support to win the London Olympic bid puts him in a good light. He found fans in former London mayor Ken Livingstone and Tessa Jowell, the shadow minister for the Olympics.

"Seb is a person of such talent that he is spoilt for choice," said Jowell. "The BBC would be very fortunate but I suspect that his heart is still in sports leadership."

Coe also enjoys strong Tory credentials. He was an MP for five years before losing his seat in the 1997 general election, returning to politics for a short time as William Hague's chief of staff after receiving a life peerage in 2000.

One source said they could not imagine Coe giving up on his long-held ambition to win the presidency of the International Association of Athletics Federations – he has been a vice president since 2007 – with the election for a successor next year.

"I cannot see him giving up on athletics," said the source. "But then why couldn't he do both, the BBC Trust role is not meant to be full time".

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